How many strings of 4 lowercase letters have the letter x in them?

Question
Factors and multiples
asked 2020-12-30
How many strings of 4 lowercase letters have the letter x in them?

Answers (1)

2020-12-31
There are 26 letters, so the total number of strings of 4 lowercase letters is
\(\displaystyle{26}^{{4}}={456},{975}\)
(in each of the four places, we can put any of the 26 letters).
On the other hand, the number of strings of 4 lowercase letters that do not have the letter x in them is
\(\displaystyle{25}^{{4}}={390},{625}\)
(in each of the four places, we can put any of the 25 letters, since we are excluding x).
Finally, the difference of these numbers is the number of strings of 4 lowercase letters that have the letter x in them:
\(\displaystyle{26}^{{4}}-{25}^{{4}}—{456.975}—{390},{625}={66},{350}\)
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